# Cointegration and Granger causality

Can anyone please tell me whether the existence of cointegration between two series necessarily implies Granger causality between their "first differences"? I'd appreciate it if you could explain your reason.

• yes. granger causality says that, if including X in a model, improves ones prediction of Y, then X granger causes Y. In the case of cointegration, the ECM formulation shows explicitly that knowing $(X_t - X_{t-1})$ improves the prediction of $(Y_t - Y_{t-1})$ which are both first differences. Apr 22 at 11:02
• @mlofton, it is always good to emphasize that Granger causality deals with incremental improvement in prediction accuracy once lags of $Y$ have been conditioned on. I have seen too many instances where people forget that and then incorrectly conclude that e.g. early-morning bird songs Granger-cause sunrise... Apr 22 at 11:38
• @Richard Hardy: Yes, I hope that I said that sort of but probably did not give it enough emphasis. The interesting thing about cointegration ( atleast in the engle-granger case where there are just two variables ) is that, as the OP said, the first difference of $X_t$ granger causes the first difference of $Y_t$. I never thought of it that way until I read the question. Apr 22 at 20:14
• Does this vary with the type of cointegration used? For example I am learning it in the context of the ARDL bounds test. Not the Engel Granger method (and still understand the concept very generally at best). I know these two approaches are quite different. Apr 22 at 21:56
• A quotation from Dave Giles blog: "If two or more time-series are cointegrated, then there must be Granger causality between them - either one-way or in both directions. However, the converse is not true.". The blog post is very well written – go ahead and read it. Perhaps you will find the answer to your question as well. Apr 23 at 5:30